If the line (2-x)/(3)=(3y-2)/(4 +1)=4-z makes a right angle with the line (x+3)/(3 )=(1-2y…

Question

If the line $\frac{2-x}{3}=\frac{3y-2}{4\lambda +1}=4-z$ makes a right angle with the line $\frac{x+3}{3\mu }=\frac{1-2y}{6}=\frac{5-z}{7}$, then $4\lambda +9\mu $ is equal to :

Accepted Answer

$\begin{gathered} {L}_{1}:\frac{x-2}{(-3)}=\frac{y-\frac{2}{3}}{(\frac{4\lambda +1}{3})}=\frac{}{(-1)} \ {L}_{2}:\frac{x+3}{3\mu }=\frac{y-\frac{1}{2}}{-3}=\frac{z-5}{-7} \ \because {L}_{1}\perp {L}_{2} \ \Rightarrow (-3)(3\mu )+(\frac{4\lambda +1}{3})(-3)+(-1)(-7)=0 \ -9\mu -4\lambda -1+7=0 \ \Rightarrow 4\lambda +9\mu =6 \end{gathered}$

Solutions · 1